(5n+0+2)(10*4n)=

Solution for (5n+0+2)(10*4n)= equation:

Simplifying
(5n + 0 + 2)(10 * 4n) = 0

Reorder the terms:
(0 + 2 + 5n)(10 * 4n) = 0

Combine like terms: 0 + 2 = 2
(2 + 5n)(10 * 4n) = 0

Multiply 10 * 4
(2 + 5n)(40n) = 0

Remove parenthesis around (40n)
(2 + 5n) * 40n = 0

Reorder the terms for easier multiplication:
40n(2 + 5n) = 0
(2 * 40n + 5n * 40n) = 0
(80n + 200n2) = 0

Solving
80n + 200n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '40n'.
40n(2 + 5n) = 0

Ignore the factor 40.
Subproblem 1
Set the factor 'n' equal to zero and attempt to solve:

Simplifying
n = 0

Solving
n = 0

Move all terms containing n to the left, all other terms to the right.

Simplifying
n = 0
Subproblem 2
Set the factor '(2 + 5n)' equal to zero and attempt to solve:

Simplifying
2 + 5n = 0

Solving
2 + 5n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + 5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5n = 0 + -2
5n = 0 + -2

Combine like terms: 0 + -2 = -2
5n = -2

Divide each side by '5'.
n = -0.4

Simplifying
n = -0.4
Solution
n = {0, -0.4}